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Two uniform machines with nearly equal speeds: unified approach to known sum and known optimum in semi on-line scheduling

Author

Listed:
  • György Dósa

    (University of Pannonia)

  • M. Grazia Speranza

    (University of Brescia)

  • Zsolt Tuza

    (University of Pannonia
    Hungarian Academy of Sciences)

Abstract

We consider semi on-line scheduling on two uniform machines. The speed of the slow machine is normalized to 1 while the speed of the fast machine is assumed to be s≥1. Jobs of size J 1,J 2,… arrive one at a time, and each J i (i≥1) has to be assigned to one of the machines before J i+1 arrives. The assignment cannot be changed later. The processing time of the ith job is J i on the slow machine and J i /s on the fast one. The objective is to minimize the makespan. We study both the case where the only information known in advance is the total size ∑i≥1 J i of the jobs and the case where the only information known in advance is the optimum makespan. For each of these two cases, we almost completely determine the best possible competitive ratio of semi on-line algorithms compared to the off-line optimum, as a function of s in the range $1\le s

Suggested Citation

  • György Dósa & M. Grazia Speranza & Zsolt Tuza, 2011. "Two uniform machines with nearly equal speeds: unified approach to known sum and known optimum in semi on-line scheduling," Journal of Combinatorial Optimization, Springer, vol. 21(4), pages 458-480, May.
    • Handle: RePEc:spr:jcomop:v:21:y:2011:i:4:d:10.1007_s10878-009-9265-2
    DOI: 10.1007/s10878-009-9265-2
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    Cited by:

    1. György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2018. "Tight upper bounds for semi-online scheduling on two uniform machines with known optimum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(1), pages 161-180, March.
    2. Leah Epstein, 2018. "A survey on makespan minimization in semi-online environments," Journal of Scheduling, Springer, vol. 21(3), pages 269-284, June.
    3. György Dósa & Armin Fügenschuh & Zhiyi Tan & Zsolt Tuza & Krzysztof Węsek, 2019. "Tight lower bounds for semi-online scheduling on two uniform machines with known optimum," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 27(4), pages 1107-1130, December.

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